Evolution of Moduli

In the rich landscape of algebraic varieties, moduli spaces stand out as some of the most enchanting varieties, capturing the imagination of algebraic geometers with their profound elegance and deep connections to other branches of mathematics.   Moduli, the plural of modulus, is a term coined by Riemann to describe a space whose points afford an alternative description as certain classes of geometric objects.  We will trace the origins of moduli spaces through the discoveries of Riemann, Hilbert, Grothendieck, Mumford, and Deligne, as a means to explain many of the fundamental concepts of moduli spaces.  We will then survey how the foundations of moduli theory have further evolved over the last 50 years.